What is the cosine of the angle which the vector 2 i^&n

Subject

Mathematics

Class

CBSE Class 12

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Sample Papers

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 Multiple Choice QuestionsShort Answer Type

1.

If A =   cosα  - sinαsinα     cosα , then for what value of α is A an identity matrix?


2.

What is the principal value of cos-1 -32 ?


3.

What is the range of the function f(x) =  x - 1  x - 1 ?


4.

Find the minor of the element of second row and third column ( a23 ) in the following determinant:

  2  -3   56   0  41   5 -7  


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5.

If  1  23  4    3  12   5   =  7   11k   23 , then write the value of k.


6.

Evaluate: log xx dx


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7.

What is the cosine of the angle which the vector 2 i^ + j^ + k  makes with y-axis?


The y-axis can be represented in vector form by j^  and -j^.

Let    a = 2 i^ + j^ + k    and    b = j^   or  -j^ cosθ = a^ . b a^   b  cosθ =  2 i^ + j^ + k  .  ± j^  2 i^ + j^ + k   .   j ^= ± 1 x 122 + 12 + 12 x 12 =  ± 1 4 =  ± 1 2So, the cosine of the  angle which the vector  2 i^ + j^ + k  makeswith y-axis is  ±12


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8.

Write a vector of magnitude 15 units in the direction of vector  i^ - 2j^ + 2k


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9.

Write the vector equation of the following line:

x - 53 = y + 47 = 6 - z2


10.

What is the degree of the following differential equation?

5x 5x dydx2 - d2ydx2 - 6y = log x


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